If n is a prime number greater than 3

If \(n\) is a prime number greater than 3, what is the remainder when \(n^2\) is divided by 12?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 5

I call these kinds of problems Theorem Problems. What I mean by that is that there is some deep mathematical rule that forms the basis of the problem. In this case that rule is about squares modulo p and quadratic residues. Neither of these is part of what the GMAT is testing – even if you’re treating the quantitative section as a math test and not a game.

Clearly someone working for GMAC is nerding out. Unfortunately for the nerd in question, and fortunately for us, mathematicians don’t do multiple choice. When you see something like this, take a deep breath and remember that PS (problems solving) questions are matching games. We just have to match the question to the answer. We don’t need math degrees.

So, pick a prime greater than 3, square it, and divide by 12. What’s the remainder?

For example, 5 is a prime greater than 3 (in fact, the smallest prime greater than three – keep it simple), \(5^2\) is 25, and when 25 is divided by 12, the remainder is 1.

The correct answer is B. It’s really that simple.

Now, an important question: Do we need to check another example? The answer is NO! There’s only one answer per question!